- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 959346, 7 pages
A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems
1School of Mathematics and Sciences, Harbin Normal University, Harbin 150025, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 23 January 2013; Revised 4 July 2013; Accepted 18 August 2013
Academic Editor: Yong Hong Wu
Copyright © 2013 Jing Niu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. Alpay, Algorithme de Schur Espaces d Noyau Veproduisant et Thgorie des Systemes, vol. 6 of Panoramas et Synthèses, Société Mathématique de France, Paris, France, 1998.
- S. D. Chatterji, “Factorization of positive finite operator-valued kernels,” in Prediction Theory and Harmonic Analysis, vol. 12, pp. 23–36, North-Holland, Amsterdam, The Netherlands, 1983.
- S. D. Chatterji, “Positive definite kernels,” Boletín de la Sociedad Matemática Mexicana, vol. 28, no. 2, pp. 59–65, 1983.
- E. Hille, “Introduction to general theory of reproducing kernels,” The Rocky Mountain Journal of Mathematics, vol. 2, no. 3, pp. 321–368, 1972.
- H. Meschkowski, Hilbertsche Räume mit Kernfunktion, Springer, Berlin, Germany, 1962.
- T. E. Voth and M. A. Christon, “Discretization errors associated with reproducing kernelmethods: one-dimensional domains,” Computer Methods in Applied Mechanics and Engineering, vol. 190, no. 18-19, pp. 2429–2446, 2001.
- M. G. Cui and F. Z. Geng, “Solving singular two-point boundary value problem in reproducing kernel space,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 6–15, 2007.
- J. Niu, Y. Z. Lin, and M. G. Cui, “Approximate solutions to three-point boundary value problems with two-space integral condition for parabolic equations,” Abstract and Applied Analysis, vol. 2012, Article ID 414612, 9 pages, 2012.
- C. P. Zhang, J. Niu, and Y. Z. Lin, “Numerical solutions for the three-point boundary value problem of nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2012, Article ID 360631, 16 pages, 2012.
- J. Du and M. Cui, “Constructive proof of existence for a class of fourth-order nonlinear BVPs,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 903–911, 2010.
- H. Long and X. J. Zhang, “Construction and calculation of reproducing kernel determined by various linear differential operators,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 759–766, 2009.
- X. J. Zhang and J. H. Huang, “The uniformity of spline interpolating operators and the best operators of interpolating approximation in spaces,” Mathematica Numerica Sinica, vol. 23, no. 4, pp. 385–392, 2001.
- M. G. Cui and B. Y. Wu, Reproducing Kernel Space Numerical Analysis, Beijing Science Press, Beijing, China, 2004.
- X. Q. Lv and M. G. Cui, “Analytic solutions to a class of nonlinear infinite delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 343, no. 2, pp. 724–732, 2008.
- M. C. Cui and Y. Z. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science, New York, NY, USA, 2009.
- Z. Chen and Y. Z. Lin, “The exact solution of a linear integral equation with weakly singular kernel,” Journal of Mathematical Analysis and Applications, vol. 344, no. 2, pp. 726–734, 2008.
- H. M. Yao and M. Cui, “Searching the least value method for solving fourth-order nonlinear boundary value problems,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 677–683, 2010.
- V. Giovangigli, “Nonadiabatic plane laminar flames and their singular limits,” SIAM Journal on Mathematical Analysis, vol. 21, no. 5, pp. 1305–1325, 1990.
- P. L. Simon, S. Kalliadasis, J. H. Merkin, and S. K. Scott, “Quenching of flame propagation with heat loss,” Journal of Mathematical Chemistry, vol. 31, no. 3, pp. 313–332, 2002.
- P. L. Simon, S. Kalliadasis, J. H. Merkin, and S. K. Scott, “Evans function analysis of the stability of non-adiabatic flames,” Combustion Theory and Modelling, vol. 7, no. 3, pp. 545–561, 2003.
- M. D. Smooke, “Solution of burner stabilized premixed laminar flames by boundaryvalue methods,” Journal of Computational Physics, vol. 48, no. 1, pp. 72–105, 1982.
- J. Niu, Y. Z. Lin, and C. P. Zhang, “Numerical solution of nonlinear three-point boundary value problem on the positive half-line,” Mathematical Methods in the Applied Sciences, vol. 35, no. 13, pp. 1601–1610, 2012.
- H. Lian and W. Ge, “Existence of positive solutions for Sturm-Liouville boundary value problems on the half-line,” Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 781–792, 2006.
- S. Djebali and K. Mebarki, “Multiple unbounded positive solutions for three-point BVPs with sign-changing nonlinearities on the positive half-line,” Acta Applicandae Mathematicae, vol. 109, no. 2, pp. 361–388, 2010.
- Y. Tian and W. Ge, “Positive solutions for multi-point boundary value problem on the half-line,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1339–1349, 2007.